9-12

enneatonic scale (Messiaen mode 3)

prime form 01245689t · vector 666963 · 4 sets

One shape, its own mirror

steps 1 1 2 1 1 2 1 1 2

range 10 · 4 transpositions · 3 modes

Interval-class vector
ic1	ic2	ic3	ic4	ic5	ic6
6	6	6	9	6	3

Every set in the class holds six semitones, six whole tones, six minor thirds, nine major thirds, six fourths and three tritones.

Common tones under Tn
T0	T1	T2	T3	T4	T5	T6	T7	T8	T9	T10	T11
9	6	6	6	9	6	6	6	9	6	6	6

Notes a set keeps when transposed by n.

Common tones under TnI
T0I	T1I	T2I	T3I	T4I	T5I	T6I	T7I	T8I	T9I	T10I	T11I
6	6	9	6	6	6	9	6	6	6	9	6

Notes a set keeps when inverted about n.

Set theory treats D# and Eb as one pitch class; the names under each set use one fixed spelling, sharps except Bb.

Complement

3-12 048 · augmented triad

Z-partner

none: no other class has this interval vector

Symmetry

3 transpositions and 3 inversions map it onto itself

Inside it

2 notes: 2-1 ×6 · 2-2 ×6 · 2-3 ×6 · 2-4 ×9 · 2-5 ×6 · 2-6 ×3

3 notes: 3-1 ×3 · 3-2 ×6 · 3-3 ×12 · 3-4 ×12 · 3-5 ×6 · 3-6 ×6 · 3-7 ×6 · 3-8 ×12 · 3-9 ×3 · 3-10 ×3 · 3-11 ×12 · 3-12 ×3

4 notes: 4-2 ×6 · 4-3 ×3 · 4-4 ×6 · 4-5 ×6 · 4-7 ×6 · 4-8 ×3 · 4-11 ×6 · 4-12 ×6 · 4-14 ×6 · 4-Z15 ×6 · 4-16 ×6 · 4-17 ×6 · 4-18 ×6 · 4-19 ×12 · 4-20 ×6 · 4-21 ×6 · 4-22 ×6 · 4-24 ×6 · 4-25 ×3 · 4-26 ×3 · 4-27 ×6 · 4-Z29 ×6

5 notes: 5-3 ×6 · 5-6 ×6 · 5-8 ×3 · 5-9 ×6 · 5-11 ×6 · 5-13 ×6 · 5-15 ×3 · 5-16 ×6 · 5-Z17 ×3 · 5-Z18 ×6 · 5-20 ×6 · 5-21 ×12 · 5-22 ×3 · 5-24 ×6 · 5-26 ×6 · 5-27 ×6 · 5-28 ×6 · 5-30 ×6 · 5-32 ×6 · 5-33 ×6 · 5-34 ×3 · 5-Z37 ×3 · 5-Z38 ×6

6 notes: 6-Z4 ×3 · 6-Z10 ×6 · 6-14 ×6 · 6-15 ×6 · 6-16 ×6 · 6-Z19 ×6 · 6-20 ×2 · 6-21 ×6 · 6-22 ×6 · 6-Z26 ×3 · 6-31 ×6 · 6-34 ×6 · 6-35 · 6-Z43 ×6 · 6-Z44 ×6 · 6-Z46 ×6 · 6-Z49 ×3

7 notes: 7-13 ×6 · 7-Z17 ×3 · 7-21 ×6 · 7-22 ×3 · 7-26 ×6 · 7-30 ×6 · 7-33 ×3 · 7-Z37 ×3

8 notes: 8-19 ×6 · 8-24 ×3

Around it

10-4 ×3 · and 2 larger classes